# Resistance equivalent to a circuit

1. Sep 29, 2009

### oswald2323

Hi,

Suppose I have the following circuit (excuse the ugly drawing):

Suppose the generator is 1A and all the resistance are 1 Ohm (the values are not important). Moreover, suppose I already have all the voltages in V1, V2, V3, V4 (which I got using nodal analysis), and V0 is set to ground (V0 = 0).

How do I get the total resistance from point A to point B (or node V0)? Can I use the results I got from nodal analysis for this?

Please note my knowledge of electrical circuits is very basic, as this is not my field. I am using this to build an artificial Hex player, and resistance provides a good connectivity measure from each side of the board (see page 2 in http://home.earthlink.net/~vanshel/VAnshelevich-01.pdf).

2. Sep 29, 2009

### The Electrician

The voltages of V1 and V2 must be the same since they are connected by a wire.

The voltages of V3 and V4 must be zero since they are connected together by a wire which is also connected to ground.

For this circuit, since you are exciting it with a current source of 1 amp, then the resistance from A to B (ground) is equal to the voltages at V1 and V2, which are the same.

3. Sep 30, 2009

### vk6kro

Any resistors you have shorted out can be replaced by wires.

That only leaves 3 resistors in parallel in the middle of the diagram.

They are all 1 ohm, so ....... what is the total resistance?

4. Sep 30, 2009

### oswald2323

Are you saying that the resistance from A to B is R = V1/I = V1 Ohm = V2 Ohm?

Also, why is the voltage the same in V1 and V2, if current can flow from A to V1 and V2? Shouldn't V1 and V2 have a lower potential than A?

@vk6kro: I wanted to avoid that kind of analysis, since this circuit is not "fixed". Its just the simplest case of a much larger circuit that may look different (resistances with value=+infinite or 0), and I want a way to solve this that is easy to code into a program that does it (an algorithm, so to speak).

Thanks!

5. Sep 30, 2009

### The Electrician

Exactly.

The voltage is the same at V1 and V2 because they are connected together by a wire.

In schematics such as you have shown, a simple line represents a wire, which is assumed to have zero resistance.

Real wires don't have zero resistance. They have some finite, non-zero resistance, but if you want to treat that in a circuit you would usually insert a resistor symbol of some low value like 500 microhms to represent the wire resistance. In the absence of any such representation of the non-zero resistance of a wire, the wire is treated as though it has zero resistance.